I am trying to solve a system of equations mod $p$, for $p$ prime. I have build matrices $A$ and $b$ and I am using the function solve_right() to solve $Ax = b$. But I need to solve $Ax = b$ mod $p$. Is there any functions that could do that ? thanks !
If you define your matrices containing elements of the field $\mathbb Z/p\mathbb Z$, solve_right does what you need.
sage: A = matrix(GF(17), [[6,3], [3,8]])
sage: b = matrix(GF(17), [1, 2]).transpose()
sage: A.solve_right(b)
[14]
[12]
If for some reason you need matrices over (say) $\mathbb Z$ but still need to solve modulo some prime $p$, you can use change_ring.
sage: A = matrix(ZZ, [[1,2], [3,4]])
sage: b = matrix(ZZ, [5, 6]).transpose()
sage: A.change_ring(GF(17)).solve_right(b.change_ring(GF(17)))
[13]
[13]
Asked: 2017-04-02 17:31:52 +0100
Seen: 4,639 times
Last updated: Apr 02 '17
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